Abstract

This paper considers the optimal investment problem in a financial market with one risk-free asset and one jump-diffusion risky asset. It is assumed that the insurance risk process is driven by a compound Poisson process and the two jump number processes are correlated by a common shock. A general mean-variance optimization problem is investigated, that is, besides the objective of terminal condition, the quadratic optimization functional includes also a running penalizing cost, which represents the deviations of the insurer’s wealth from a desired profit-solvency goal. By solving the Hamilton-Jacobi-Bellman (HJB) equation, we derive the closed-form expressions for the value function, as well as the optimal strategy. Moreover, under suitable assumption on model parameters, our problem reduces to the classical mean-variance portfolio selection problem and the efficient frontier is obtained.

Highlights

  • In the past two decades, the problems of optimal investment and optimal reinsurance have gained rich attention in actuarial and financial literature

  • Bäuerle (2005) first put forward that the criterion of mean-variance may be attractive in insurance applications and investigated optimal reinsurance strategy when the insurance risk process is described by a classical compound Poisson process

  • The second frequently-used model describes that financial market and insurance risk are dependent with each other, i.e., the risky asset and insurance claims are correlated by a common shock

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Summary

Introduction

In the past two decades, the problems of optimal investment and optimal reinsurance have gained rich attention in actuarial and financial literature. The second frequently-used model describes that financial market and insurance risk are dependent with each other, i.e., the risky asset and insurance claims are correlated by a common shock Based on this kind of common shock, Liang et al (2016, 2017) studied the optimal reinsurance-investment problems under the mean-variance and exponential utility criterion, respectively. Zhang and Liang (2017) investigated the optimal investment strategy under the criterion of maximizing the mean-variance utility with state dependent risk aversion. This paper considers a running penalizing cost, with a deterministic goal process to be achieved for the insurer and extends the existing results of the classical mean-variance problem As is known, this results in the optimization problem with wealth-path dependence (see Bouchard and Pham (2004)).

Some Necessary Notations
Description of Financial Market
Problem Formulation
The Closed-Form Solution to HJB Equation
Efficient Strategy and Efficient Frontier
Sensitive Analysis
Conclusions
Full Text
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